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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Extreme Synergy in the Random-Energy Model.

Vudtiwat Ngampruetikorn1,2, David J Schwab2

  • 1School of Physics, <a href="https://ror.org/0384j8v12">University of Sydney</a>, Sydney, NSW 2006, Australia.

Physical Review Letters
|January 3, 2025
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Summary
This summary is machine-generated.

The random-energy model (REM) demonstrates extreme synergy, enabling a novel secure secret-sharing scheme. This statistical physics model offers optimal information encoding and connects physics to computation.

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Area of Science:

  • Statistical Physics
  • Information Theory
  • Computational Science

Background:

  • The random-energy model (REM) is a solvable spin-glass model with broad applications.
  • Previous applications span protein folding, combinatorial optimization, and many-body localization.
  • A novel connection between REM and secret sharing is explored.

Purpose of the Study:

  • To derive an analytic expression for mutual information between REM subsystems.
  • To formulate a secret-sharing scheme based on REM correlations.
  • To determine conditions for secure secret sharing within the REM framework.

Main Methods:

  • Derivation of analytic expression for mutual information.
  • Formulation of a secret-sharing scheme using REM.
  • Analysis of temperature and secret length parameters for security.
  • Investigation of a special point for optimal information encoding.

Main Results:

  • REM correlations exhibit extreme synergy, analogous to secure secret sharing.
  • Specific temperature and secret length ranges for REM security were identified.
  • A physically optimal information encoding point in the REM phase diagram was found.
  • Thermodynamic limit results align qualitatively with finite system simulations.

Conclusions:

  • The REM provides a framework for secure secret sharing with optimal encoding properties.
  • Synergistic correlations in many-body systems can be characterized using this new language.
  • Information theory serves as a unifying concept linking statistical physics and computation.